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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 126 · 40 questions
TalentJR

How to solve it (Factors come in pairs): Find factors in pairs: 1 × N, 2 × …, 3 × …, until the pairs meet. Prime factorisation: keep dividing by the smallest prime that works, then group equal primes as powers. 1 is not a prime; 2 is the only even prime. To test a number, try dividing by the primes up to its square root.

NameDateTime takenScore ___ / 40
  1. 1.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 7 (d) 6
  2. 2.How many factors does 78 have? (a) 8 (b) 7 (c) 9 (d) 6
  3. 3.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 11 (d) 1
  4. 4.How many factors does 23 have? (a) 1 (b) 4 (c) 2 (d) 3
  5. 5.How many factors does 96 have? (a) 11 (b) 12 (c) 10 (d) 13
  6. 6.What is the smallest prime factor of 85? (a) 2 (b) 5 (c) 1 (d) 17
  7. 7.How many factors does 108 have? (a) 13 (b) 11 (c) 10 (d) 12
  8. 8.What is the smallest prime factor of 341? (a) 31 (b) 2 (c) 1 (d) 11
  9. 9.What is the smallest prime factor of 217? (a) 1 (b) 2 (c) 31 (d) 7
  10. 10.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 3 (d) 1
  11. 11.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 5 (d) 2
  12. 12.How many factors does 42 have? (a) 9 (b) 8 (c) 6 (d) 7
  13. 13.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 9 (d) 7
  14. 14.How many factors does 15 have? (a) 3 (b) 4 (c) 2 (d) 5
  15. 15.How many factors does 41 have? (a) 4 (b) 1 (c) 2 (d) 3
  16. 16.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  17. 17.How many factors does 50 have? (a) 4 (b) 5 (c) 7 (d) 6
  18. 18.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 4 (d) 1
  19. 19.What is the smallest prime factor of 247? (a) 1 (b) 2 (c) 19 (d) 13
  20. 20.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2 × 3² (d) 2³ × 3
  21. 21.How many factors does 57 have? (a) 5 (b) 3 (c) 2 (d) 4
  22. 22.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 11 (d) 13
  23. 23.How many factors does 112 have? (a) 10 (b) 8 (c) 9 (d) 11
  24. 24.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  25. 25.How many factors does 107 have? (a) 2 (b) 3 (c) 4 (d) 1
  26. 26.How many factors does 90 have? (a) 11 (b) 12 (c) 13 (d) 10
  27. 27.How many factors does 16 have? (a) 6 (b) 5 (c) 3 (d) 4
  28. 28.How many factors does 14 have? (a) 4 (b) 5 (c) 3 (d) 2
  29. 29.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
  30. 30.What is the smallest prime factor of 221? (a) 2 (b) 17 (c) 13 (d) 1
  31. 31.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
  32. 32.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 6 (d) 5
  33. 33.How many factors does 74 have? (a) 5 (b) 3 (c) 2 (d) 4
  34. 34.What is the smallest prime factor of 299? (a) 2 (b) 23 (c) 13 (d) 1
  35. 35.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 4 (d) 2
  36. 36.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 13 (d) 1
  37. 37.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 5 (d) 6
  38. 38.How many factors does 24 have? (a) 6 (b) 9 (c) 7 (d) 8
  39. 39.What is the prime factorisation of 18? (a) 2² × 3² (b) 2² × 3 (c) 2 × 3³ (d) 2 × 3²
  40. 40.How many prime numbers are there between 40 and 50? (a) 5 (b) 4 (c) 3 (d) 2

Answer key

  1. 7
  2. 8
  3. 7
  4. 2
  5. 12
  6. 5
  7. 12
  8. 11
  9. 7
  10. 3
  11. 5
  12. 8
  13. 7
  14. 4
  15. 2
  16. 4
  17. 6
  18. 2
  19. 13
  20. 2² × 3
  21. 4
  22. 11
  23. 10
  24. 3² × 5 × 7
  25. 2
  26. 12
  27. 5
  28. 4
  29. 7
  30. 13
  31. 2⁴ × 3
  32. 6
  33. 4
  34. 13
  35. 2
  36. 13
  37. 4
  38. 8
  39. 2 × 3²
  40. 3

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